In a white dwarf, each electron can be considered to be located in a region of size 1.5x10-12 m. Estimate the minimum speed of the electron (with respect to the speed of light c).
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- The expanding universe is carrying distant objects away from each other at a rate proportional to their separations. We use the Doppler effect observed in spectra of distant galaxies and quasars to calculate recession speeds. For the most distant objects recession speeds approach c, and therefore, the relativistic Doppler shift expression must be used. We define the redshift, z, as the fractional change in wavelength. a) The most distant quasar currently known is ULAS J1120+0641, discovered with the UK Infrared Telescope on Mauna Kea. It has a redshift of 7.1. Calculate its radial velocity in terms of v/c. b) Determine the distance to this quasar. c) At what wavelength would the Ha line (656.28 nm) be observed for this quasar?1) Derive the radial probability for the 3p orbital. Calculate the maxima and minima, and graph the radial probability for the 3p. Y3p(R) = constant * R * ( 4 – 2ZR/3a0) * exp(−ZR/3a0)A blackbody at a temperature of 5000 K emits radiation. Calculate the wavelength at which the intensity of the emitted radiation is maximum, according to Wien's displacement law. The value of Wien's constant is approximately 2.898 × 10^(-3) m·K.
- The rest wavelength of the Hα transition of atomic hydrogen is 656.3 nm (recall that 1 nm=10-9 m). If an observer takes a spectrum of a distant galaxy and identifies that line at 920 nm, what is the redshift of the galaxy? (recall that z=(λobs-λem)/λem ) If the value of the Hubble constant is Ho=71 km/s/Mpc, what is the approximate distance to the galaxy in Mpc?What is the equation of the sphere with center (1, -2, 5) and radius 9? O (x +1)? + (y – 2)² + (z+5)² = 81 O (r – 1)? + (y + 2)² + (z – 5)² = 81 O x? +y? + z? = 81 O (r – 1)? + (y + 2)² + (z – 5)² = 9 O (r+1)? + (y – 2)² + (z+ 5)² = 9The CaII H and K lines have rest wavelengths of 396.85 nm and 393.36 nm, respectively. In the spectrum of a galaxy in the cluster Abell 2065, the observed wavelengths of the two lines are 425.50 nm and 421.76 nm. a) What is the redshift z of the galaxy? b) What is the distance to the galaxy? c) What is the distance modulus of the galaxy?
- A neutral pion moving with velocity v decays into two photons; one photon of energy E1 travellmng m the original direction of the parent pion and the other photon of energy E2 in the exactly opposite direction. If E1 = 2E2, find v.Of 1.5, 3, 5, and 10 give the maximum apparent speeds. 2. Consider a relativistic jet with an angle of 70 degrees relative to the line of sight (i.e. it is almost, but not quite perpendicular to the line of sight). Let its value of gamma for the motion be 3. (a) Will it appear superluminal? (b) Will it appear to be brighter or fainter than it would in its own rest frame? 3. State whether the following reactions are possible under special relativity. If not, explainTrue or false The escape speed from a black hole would be greater than the speed of light. If the impact time of a collision is increased, the force of impact will decrease. A size of a Kelvin degree (oK) is larger than a Celsius degree (oC).
- (a) Let L be the diameter of our galaxy.Suppose that a person in a spaceship of massm wants to travel across the galaxy at constantspeed, taking proper time τ. Find the kineticenergy of the spaceship. (b) Your friend is impa-tient, and wants to make the voyage in an hour.For L = 105 light years, estimate the energy inunits of megatons of TNT (1 megaton=4×109 J).A beam of π+meson (pions) at Fermilab are traveling at a speed of 0.92cwithrespect to the laboratory. The proper mean lifetime for these pions is 2.6×10−8s.(a) Is this proper lifetime measured in the laboratory frame or the frame of the pions?Why? (b) What is the mean lifetime as measured in the other frame of reference?Consider an ultrahigh-energy cosmic ray entering the Earth’s atmosphere (some have energies approaching a joule).Construct a problem in which you calculate the energy of the particle based on the number of particles in an observed cosmic ray shower. Among the things to consider are the average mass of the shower particles, the average number per square meter, and the extent (number of square meters covered) of the shower. Express the energy in eV and joules.